[For the entire collection see Zbl 0743.00067.]
J. Lannes [Homotopy theory, Proc. Symp., Durham 1985, Lond. Math. Soc. Lect. Note Ser. 117, 97-116 (1987; Zbl 0654.55013)] has treated new results (underlying topological ones) about \(H^*(V)\), the \({}\bmod p\) cohomology of an elementary abelian \(p\)-group \(V\), viewed as an object in \({\mathcal U}_ p\), the category of unstable modules over the Steenrod algebra \(A_ p\). He considers the functor \(T_ V: {\mathcal U}_ p\to{\mathcal U}_ p\), left adjoint to \(H^*(V)\otimes_ -\). The present paper gives an exposition of \(T_ V\) and its properties from the point of view of a representation theoretic framework for understanding Steenrod algebra “technology”. Four properties of \(T_ V\) (considered as fundamental by the author) are stated and new insights into the interdependence of these are given.